Aspects of operator theory in hereditarily indecomposable Banach spaces

We examine certain special features exhibited by various classes of linear operators acting in a hereditarily indecomposable Banach space. For instance, we show that the family of all Riesz operators in a H.I. space forms a closed, 2-sided ideal. We also give further characterizations of the class of scalar-type spectral operators (to those already given in [16]). The final section discusses some properties of the spectral maximal spaces of (necessarily decomposable) linear operators in such spaces. Conferenza tenuta il 16 settembre 1997 The support of the German Academic Exchange Scheme (DAAD) is gratefully acknowledged     

Heavy Majorana neutrinos in e + e − → W + W−

In this paper we investigate the effects of heavy Majorana neutrinos in the reaction e ⁺ e ^? → W ⁺ W ^?. We consider neutrino masses in the 1–10 TeV region. We show that at LEP II and NLC energies it is possible to use this processes to verify indirect evidence of heavy neutral particles with mixing angles of the order sin² α = 0.01. We discuss the unitarity restrictions that can be obtained for vector singlet and fermion-mirror-fermion models.     

A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian

A Lieb-Thirring-Sobolev type inequality for Pauli Hamiltonians with magnetic fields is derived. The bound is in terms of an effective field, whose energy is comparable to that of the magnetic field itself. An application to the stability of matter in magnetic fields is given. Received: 19 September 1996 / Accepted: 3 January 1997     

The accurate dimensional measurements within small internal structures

This paper shows that the dimension of internal structure of a component can be measured remotely to a resolution better than 5 μm by use of the combination of high resolution optical microscopy and image processing.A specialised high resolution, long working distance and diffraction limited lens was used to image within the component. A series of digital images were made to map spatially the interior of the component. An edge detector was then used to localise the specific location of features in order that an accurate internal measurement could be made. A visualisation of the internal surface finish was also achieved.     

Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators     

Resonance enhancement of diffuse scattering of x-rays in a waveguide heterostructure

The diffuse scattering of x rays in a four-layer waveguide-type heterostructure is investigated. The dynamic enhancement of diffuse scattering is detected experimentally in regions corresponding to the excitation of waveguide modes for both the incident and scattered waves. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 219–223 (25 August 1997)     

Phase shift moiré studies of processing-induced residual strains in Nickel 200 spot welds

Processing-induced residual strains in solid cylinders of Nickel 200 were investigated using phase shifting moiré interferometry. Two different experimental approaches were used to study the strains produced during Tungsten-inert gas spot welding. A comparison of results for a ‘hot/fast’ and a ‘cool/slow’ weld demonstrate the capabilities of the general approach. Both experimental methods revealed distinct differences in the residual displacement and strain fields between the two types of welds.     

On the connectedness of numerical range of matrix polynomials

An investigation on nonconnectedness of numerical range for monic matrix polynomials L(λ) is undertaking here. The distribution of eigenvalues of L(λ) to the components of numerical range and some other algebraic properties are also presented.     

Recombination of Au25+ with free electrons at low energies

The origin of the widely observed enhancement of rates for electron-ion recombination at very low energies is still unknown. We investigated the recombination of Au²⁵⁺ with free electrons in a merged-beams experiment at the UNILAC accelerator of the GSI in Darmstadt. At E _rel= 0 eV we found an enormous enhancement factor of 365 compared to the theory of radiative recombination. An increase of the electron density by a factor of 10 had not much influence on the measured rate coefficient. This revised version was published online in July 2006 with corrections to the Cover Date.